.TH ZPTCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZPTCON - the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF .SH SYNOPSIS .TP 19 SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO ) .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 DOUBLE PRECISION ANORM, RCOND .TP 19 .ti +4 DOUBLE PRECISION D( * ), RWORK( * ) .TP 19 .ti +4 COMPLEX*16 E( * ) .SH PURPOSE ZPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as .br RCOND = 1 / (ANORM * norm(inv(A))). .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 D (input) DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF. .TP 8 E (input) COMPLEX*16 array, dimension (N-1) The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by ZPTTRF. .TP 8 ANORM (input) DOUBLE PRECISION The 1-norm of the original matrix A. .TP 8 RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine. .TP 8 RWORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .SH FURTHER DETAILS The method used is described in Nicholas J. Higham, "Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.